Ground bevel and hypoid gears have a designed motion error that defines parts of their noise vibration harshness (NVH) behavior. In addition to other dynamic effects, the surface structure has an effect on the excitation behavior. This surface structure is defined via a hard finishing process. Very common hard finishing processes are, for example, lapping, grinding and skiving. Grinding shows the advantage of high repeatability, defined flank forms with closed loop corrections and subsequently have very low reject rates. However it is known that, for example, lapped gear sets show, at least at low loads, a lower excitation level including the lower as well as the higher mesh harmonics.
In producing gears by a generating process, a tool and a workpiece are rolled together in a predetermined relative rolling motion, known as a generating roll, as though the workpiece were rotating in mesh with a theoretical generating gear, the teeth of the theoretical generating gear being represented by the stock removing surfaces of the tool. The profile shape of the tooth is formed (i.e. generated) by the relative motion of the tool and workpiece during the generating roll. Usually, the tool is a cup-shaped grinding wheel or a cutting tool comprising a disc-shaped cutter head with a plurality of cutting blades projecting from a face of the cutter head.
Generating grinding for bevel ring gears or pinions presents the grinding wheel as a tooth of the theoretical generating gear, while the workpiece rolls on the generating gear tooth to finish the profile and lead of the workpiece tooth surface. During the generating roll, a computer controlled (e.g. CNC) free form machine, such as disclosed in U.S. Pat. No. 6,712,566 (incorporated herein by reference) for example, changes its axes positions in several hundred steps with each step represented by up to three linear axis positions (e.g. X, Y, Z) and up to three rotational axis positions (e.g. tool, workpiece, pivot) of the machine. In generating grinding of bevel and hypoid gears, five axes are commonly required (the grinding wheel rotates independently), which change their axis positions several hundred times during the rolling process for each tooth surface.
FIG. 1 illustrates an example of the contact between a grinding wheel and a tooth surface 2 in a generating process. As mentioned above, during the generating process, the positions of the machine axes are usually changed several hundred times during grinding of a tooth surface as the grinding wheel is traversed across the tooth surface during the generating roll. Each positional change may be represented by a contact line Lc with the lines of contact being oriented at an inclination angle αt. The number of contact lines m (i.e. the number of axes positional changes) per each generating roll position may vary but for discussion purposes only, 300 contact lines will be referenced although it should be understood that fewer or more lines of contact may be utilized. The area F between successive lines of contact shall be referred to as a “flat” or “facet”. Thus, for a generating roll consisting of 300 lines of contact, 299 flats will be generated.
In practice, the flats of ground gears are extremely small (referred to as micro flats) and are usually not visible to the eye due to the grinding wheel surface effectively being a continuum surface with no discreet and defined cutting surfaces as would be found with a cutting tool having cutter blades. In comparison, flats of gear tooth flanks produced by cutting, particularly rough cut gears, may be more pronounced and visible. It can therefore be appreciated that for a certain machining process, machining flats specific to the particular process (e.g. grinding, cutting) are produced on a gear tooth flank. The existence of flats and the knowledge that different machining processes produce respective types of flats (i.e. machining-specific flats) are, per se, known to the skilled artisan.
As descried, the motions between tool and work gear are typically derived from a rolling process of the work gear and the generating gear. With the more recent transformation of the rolling motion into a five or six axis free-form machine (such as, for example, U.S. Pat. No. 6,712,566), the motions of the single axes are basically third order functions with a dominating first order content. The coordinates for all axes are written into an axis position table that is read in by the machine controller of the free-form machine.
The generation of a ground pinion is realized via the rolling motion of a cup-shaped grinding wheel that follows a path given by the axis position table. Some excitations in ground gear sets are caused by the production process itself. The machine follows each line in this axis position table and interpolates between the lines. At low roll rates, a high number of lines are given in the axis position table and the machine can follow these lines very accurately because of the slow motions and their continuous functions. Also with low roll rates, the machine inertia contributes to smooth transitions between the lines in the axis position table.
At high roll rates, fewer lines are generated in the axis position table. The machine has to follow these lines at a higher speed while the grinding wheel revolutions per minute (RPM), determined from a given surface speed, remains the same. This results in fewer revolutions of the grinding wheel between the axis positions of the part program, creating a surface pattern similar to generating flats formed during a cutting process. The minimal time increment between two axis positions is limited by the controller specific block time, which presents the upper limit of axis positions for each given roll rate.
The above described effects can basically be summarized as influences where machine motions itself in combination with resulting machine vibrations and imperfect grinding wheel roundness during a standard grinding process will lead to a distinct surface structure with facets parallel to the contacting lines. These lines including their waviness are crossed while rolling along the path of contact and lead to excitations when rolling the bevel gear set. Depending on the roll rate and machine dynamics, these effects can be found at lower mesh harmonics (fast roll-rates) or at higher mesh harmonics (slow roll-rates).
In the process to finish bevel gears to produce a diffuse surface structure according to U.S. Pat. No. 7,462,092, the disclosure of which is hereby incorporated by reference, it is possible to influence each axis position in each line of the axis position table by small predetermined or random amounts. In previous research, this process was used to introduce a predictable and/or random surface structure on the tooth flank to influence the NVH-behavior of the ground gear set. In the standard grinding process the same axis position table is used for every tooth slot, leading to a similar appearance of the surface structure for every flank if the process affected wear of the grinding wheel from the first to last slot is neglected.
Additionally, it is known to utilize the principles of modulation (such as frequency modulation for example) in the field of mechanical engineering to influence excitation behavior. For example, in fans (U.S. Pat. No. 3,006,604), torque converters (US 2011/0289909) and turbines (U.S. Pat. No. 1,502,903), unequal spacing of the blades leads to a change in excitation behavior. FIG. 2 shows the exaggerated example of a cooling fan with unequally spaced blades. The results of these spacing variations lower the peak harmonics (e.g. blade impact frequency of a fan) and introduce additional sidebands. The energy of the peak harmonic is distributed from the peak to the sidebands leading to a lowering of the peak harmonic. This idea applied to the spacing of gear teeth has been part of several research projects but showed only limited success.
The above stated properties of the standard grinding process including the discussed process to produce a diffuse surface structure repeat precisely from one tooth to the next and may lead to excitations of discrete harmonics that correlate to the machined existing surface structure including the surface waviness, leading to measured NVH-behaviors which may not be acceptable in the final application of many ground gear sets.